Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, Cilt: 50 Sayı: 1, 199 - 215, 04.02.2021
https://doi.org/10.15672/hujms.683997

Öz

Kaynakça

  • [1] G. Anatriello, Iterated grand and small Lebesgue spaces, Collect. Math. 65, 273–284, 2014.
  • [2] R. Akgün, Trigonometric approximation of functions in generalized Lebesgue spaces with variable exponent, Ukrainian Math. J. 63 (1), 1–26, 2011.
  • [3] R. Akgün, Approximating polynomials for functions of weighted Smirnov-Orlicz spaces, J. Funct. Spaces Appl. 2012, Art. ID 982360, 2012.
  • [4] R. Akgün and D.M. Israfilov, Approximation and moduli of smoothness of fractional order in Smirnov-Orlicz spaces, Glas. Mat. Ser. III, 42 (2), 121–136, 2008.
  • [5] R. Akgün and D.M. Israfilov, Polynomial approximation in weighted Smirnov Orlicz space, Proc. A. Razmadze Math. Inst. 139, 89–92, 2005.
  • [6] R. Akgün and D.M. Israfilov, Approximation by interpolating polynomials in Smirnov- Orlicz class, J. Korean Math. Soc. 43 (2), 413–424, 2006.
  • [7] R. Akgün and D.M. Israfilov, Simultaneous and converse approximation theorems in weighted Orlicz spaces, Bull. Belg. Math. Soc. 17 (2), 13–28, 2010.
  • [8] R. Akgün and V. Kokilashvili, On converse theorems of trigonometric approximation in weighted variable exponent Lebesgue spaces, Banach J. Math. Anal. 5 (1), 70-82, 2011.
  • [9] I. Aydin, Weighted variable Sobolev spaces and capacity, J. Funct. Spaces Appl. 2012, Art. ID 132690, 2012.
  • [10] D. Cruz-Uribe and A. Fiorenza, Variable Lebesgue Spaces: Foundations and Har- monic Analysis (Applied and Numerical Harmonic Analysis), Birkhäuser/Springer, Heidelberg, 2013.
  • [11] D. Cruz-Uribe, L. Diening and P. Hästö, The maximal operator on weighted variable Lebesgue spaces, Fract. Calc. Appl. Anal. 14 (3), 361–374, 2011.
  • [12] N. Danelia and V. Kokilashvili, Approximation by trigonometric polynomials in the framework of variable exponent Lebesgue spaces, Georgian Math. J. 23 (1), 43–53, 2016.
  • [13] L. Diening, Maximal function on generalized Lebesgue spaces Lp(.), Math. Inequal. Appl. 7, 245–253, 2004.
  • [14] L. Diening, P. Harjulehto, P. Hästö and M. Ruzicka, Lebesgue and Sobolev Spaces with Variable Exponents, Lecture Notes in Mathematics, 2017, Springer, Heidelberg, 2011.
  • [15] V.K. Dzyadyk and I.A. Shevchuk, Theory of Uniform Approximation of Functions by Polynomials, Walter de Gruyter GmbH & Co. KG, 10785 Berlin, Germany, 2008.
  • [16] A. Fiorenza, B. Gupta and P. Jain, The maximal theorem in weighted grand Lebesgue spaces, Studia Math. 188 (2), 123–133, 2008.
  • [17] A. Fiorenza, V. Kokilashvili and A. Meskhi, Hardy-Littlewood maximal operator in weighted grand variable exponent Lebesgue space, Mediterr. J. Math. 14 (118), 2017.
  • [18] L. Greco, T. Iwaniec and C. Sbordone, Inverting the p-harmonic operator, Manuscripta Math. 92, 249–258, 1997.
  • [19] D.M. Israfilov and R. Akgün, Approximation in weighted Smirnov-Orlicz classes, J. Math. Kyoto Univ. 46 (4), 755–770, 2006.
  • [20] D.M. Israfilov and A. Testici, Approximation in weighted generalized grand Lebesgue spaces, Colloq. Math. 143, 113–126, 2016.
  • [21] D.M. Israfilov and A. Testici, Approximation in weighted generalized grand Smirnov spaces, Studia Sci. Math. Hungar. 54 (4), 471–488, 2017.
  • [22] T. Iwaniec and C. Sbordone, On integrability of the Jacobien under minimal hypothe- ses, Arch. Ration. Mech. Anal. 119, 129–143, 1992.
  • [23] V. Kokilashvili and A. Meskhi, Maximal and Calderon-Zygmund operators in grand variable exponent Lebesgue spaces, Georgian Math. J. 21, 447–461, 2014.
  • [24] O. Kováčik and J. Rákosník, On spaces $L^{p(x)}$ and $W^{k,p(x)}$, Czechoslovak Math. J. 41 (116), 592–618, 1991.
  • [25] W. Orlicz. Über konjugierte exponentenfolgen, Stud. Math. 3, 200–211, 1931.
  • [26] R.A. De Vore and G.G. Lorentz, Constructive Approximation, Springer, 1993.
  • [27] A. Zygmund, Trigonometric Series, Volume I-II, Cambridge University Press, Cam- bridge, 1968.

Weighted variable exponent grand Lebesgue spaces and inequalities of approximation

Yıl 2021, Cilt: 50 Sayı: 1, 199 - 215, 04.02.2021
https://doi.org/10.15672/hujms.683997

Öz

In this paper we discuss and investigate trigonometric approximation in weighted grand variable exponent Lebesgue spaces. We also prove the direct and inverse theorems in these spaces.

Kaynakça

  • [1] G. Anatriello, Iterated grand and small Lebesgue spaces, Collect. Math. 65, 273–284, 2014.
  • [2] R. Akgün, Trigonometric approximation of functions in generalized Lebesgue spaces with variable exponent, Ukrainian Math. J. 63 (1), 1–26, 2011.
  • [3] R. Akgün, Approximating polynomials for functions of weighted Smirnov-Orlicz spaces, J. Funct. Spaces Appl. 2012, Art. ID 982360, 2012.
  • [4] R. Akgün and D.M. Israfilov, Approximation and moduli of smoothness of fractional order in Smirnov-Orlicz spaces, Glas. Mat. Ser. III, 42 (2), 121–136, 2008.
  • [5] R. Akgün and D.M. Israfilov, Polynomial approximation in weighted Smirnov Orlicz space, Proc. A. Razmadze Math. Inst. 139, 89–92, 2005.
  • [6] R. Akgün and D.M. Israfilov, Approximation by interpolating polynomials in Smirnov- Orlicz class, J. Korean Math. Soc. 43 (2), 413–424, 2006.
  • [7] R. Akgün and D.M. Israfilov, Simultaneous and converse approximation theorems in weighted Orlicz spaces, Bull. Belg. Math. Soc. 17 (2), 13–28, 2010.
  • [8] R. Akgün and V. Kokilashvili, On converse theorems of trigonometric approximation in weighted variable exponent Lebesgue spaces, Banach J. Math. Anal. 5 (1), 70-82, 2011.
  • [9] I. Aydin, Weighted variable Sobolev spaces and capacity, J. Funct. Spaces Appl. 2012, Art. ID 132690, 2012.
  • [10] D. Cruz-Uribe and A. Fiorenza, Variable Lebesgue Spaces: Foundations and Har- monic Analysis (Applied and Numerical Harmonic Analysis), Birkhäuser/Springer, Heidelberg, 2013.
  • [11] D. Cruz-Uribe, L. Diening and P. Hästö, The maximal operator on weighted variable Lebesgue spaces, Fract. Calc. Appl. Anal. 14 (3), 361–374, 2011.
  • [12] N. Danelia and V. Kokilashvili, Approximation by trigonometric polynomials in the framework of variable exponent Lebesgue spaces, Georgian Math. J. 23 (1), 43–53, 2016.
  • [13] L. Diening, Maximal function on generalized Lebesgue spaces Lp(.), Math. Inequal. Appl. 7, 245–253, 2004.
  • [14] L. Diening, P. Harjulehto, P. Hästö and M. Ruzicka, Lebesgue and Sobolev Spaces with Variable Exponents, Lecture Notes in Mathematics, 2017, Springer, Heidelberg, 2011.
  • [15] V.K. Dzyadyk and I.A. Shevchuk, Theory of Uniform Approximation of Functions by Polynomials, Walter de Gruyter GmbH & Co. KG, 10785 Berlin, Germany, 2008.
  • [16] A. Fiorenza, B. Gupta and P. Jain, The maximal theorem in weighted grand Lebesgue spaces, Studia Math. 188 (2), 123–133, 2008.
  • [17] A. Fiorenza, V. Kokilashvili and A. Meskhi, Hardy-Littlewood maximal operator in weighted grand variable exponent Lebesgue space, Mediterr. J. Math. 14 (118), 2017.
  • [18] L. Greco, T. Iwaniec and C. Sbordone, Inverting the p-harmonic operator, Manuscripta Math. 92, 249–258, 1997.
  • [19] D.M. Israfilov and R. Akgün, Approximation in weighted Smirnov-Orlicz classes, J. Math. Kyoto Univ. 46 (4), 755–770, 2006.
  • [20] D.M. Israfilov and A. Testici, Approximation in weighted generalized grand Lebesgue spaces, Colloq. Math. 143, 113–126, 2016.
  • [21] D.M. Israfilov and A. Testici, Approximation in weighted generalized grand Smirnov spaces, Studia Sci. Math. Hungar. 54 (4), 471–488, 2017.
  • [22] T. Iwaniec and C. Sbordone, On integrability of the Jacobien under minimal hypothe- ses, Arch. Ration. Mech. Anal. 119, 129–143, 1992.
  • [23] V. Kokilashvili and A. Meskhi, Maximal and Calderon-Zygmund operators in grand variable exponent Lebesgue spaces, Georgian Math. J. 21, 447–461, 2014.
  • [24] O. Kováčik and J. Rákosník, On spaces $L^{p(x)}$ and $W^{k,p(x)}$, Czechoslovak Math. J. 41 (116), 592–618, 1991.
  • [25] W. Orlicz. Über konjugierte exponentenfolgen, Stud. Math. 3, 200–211, 1931.
  • [26] R.A. De Vore and G.G. Lorentz, Constructive Approximation, Springer, 1993.
  • [27] A. Zygmund, Trigonometric Series, Volume I-II, Cambridge University Press, Cam- bridge, 1968.
Toplam 27 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

İsmail Aydın 0000-0001-8371-3185

Ramazan Akgün 0000-0001-6247-8518

Yayımlanma Tarihi 4 Şubat 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 50 Sayı: 1

Kaynak Göster

APA Aydın, İ., & Akgün, R. (2021). Weighted variable exponent grand Lebesgue spaces and inequalities of approximation. Hacettepe Journal of Mathematics and Statistics, 50(1), 199-215. https://doi.org/10.15672/hujms.683997
AMA Aydın İ, Akgün R. Weighted variable exponent grand Lebesgue spaces and inequalities of approximation. Hacettepe Journal of Mathematics and Statistics. Şubat 2021;50(1):199-215. doi:10.15672/hujms.683997
Chicago Aydın, İsmail, ve Ramazan Akgün. “Weighted Variable Exponent Grand Lebesgue Spaces and Inequalities of Approximation”. Hacettepe Journal of Mathematics and Statistics 50, sy. 1 (Şubat 2021): 199-215. https://doi.org/10.15672/hujms.683997.
EndNote Aydın İ, Akgün R (01 Şubat 2021) Weighted variable exponent grand Lebesgue spaces and inequalities of approximation. Hacettepe Journal of Mathematics and Statistics 50 1 199–215.
IEEE İ. Aydın ve R. Akgün, “Weighted variable exponent grand Lebesgue spaces and inequalities of approximation”, Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 1, ss. 199–215, 2021, doi: 10.15672/hujms.683997.
ISNAD Aydın, İsmail - Akgün, Ramazan. “Weighted Variable Exponent Grand Lebesgue Spaces and Inequalities of Approximation”. Hacettepe Journal of Mathematics and Statistics 50/1 (Şubat 2021), 199-215. https://doi.org/10.15672/hujms.683997.
JAMA Aydın İ, Akgün R. Weighted variable exponent grand Lebesgue spaces and inequalities of approximation. Hacettepe Journal of Mathematics and Statistics. 2021;50:199–215.
MLA Aydın, İsmail ve Ramazan Akgün. “Weighted Variable Exponent Grand Lebesgue Spaces and Inequalities of Approximation”. Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 1, 2021, ss. 199-15, doi:10.15672/hujms.683997.
Vancouver Aydın İ, Akgün R. Weighted variable exponent grand Lebesgue spaces and inequalities of approximation. Hacettepe Journal of Mathematics and Statistics. 2021;50(1):199-215.